TL;DR: I'd recommend getting a bluetooth dongle!
I've got an Asus bluetooth 4.0 dongle, and it works perfectly for bluetooth. PS5 controllers, Airpods Pros, they've all connected to it really nicely.
I used to have issues on Windows with bluetooth, but then I found out why. My Windows was using my motherboard BT instead of the dongle. I added a PS5 controller while that was in effect, and once I eventually got the bluetooth dongle (poor BT module in the motherboard sucked ass), I noticed I couldn't remove the controller from the settings menu or through the old control panel way.
I had to turn on the BT module on my motherboard again, boot into Windows, remove the BT entries, then turn it back off. I've never had an issue in either Windows or Linux after that.